Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras

TL;DR

This paper proves quantifier elimination and rectilinearisation theorems for a broad class of generalised quasianalytic algebras of real functions, advancing the understanding of their structure.

Contribution

It establishes quantifier elimination and rectilinearisation results for generalised quasianalytic algebras, extending previous work to a more general class of function germs.

Findings

Quantifier elimination for generalised quasianalytic algebras

Rectilinearisation theorem proven for these algebras

Enhanced understanding of the structure of quasianalytic function germs

Abstract

An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.